Regression Analysis for Multiplicative Phenomena and its Implication for the Measurement of Investment Risk

Beta—the systematic risk—is generally accepted as a measure for the risk involved in holding a portfolio of risky securities. It will be shown in this paper that, because beta is measured by regressing one multiplicative variable (the rate of return of a security or a portfolio) on another multiplicative variable (the market), in the long run, the systematic risk will approach either zero or infinity. It will also be shown that in the long run the unsystematic risk will dominate the systematic risk, and that, regardless of the value of this latter risk. This implies that for investors with long planning horizon the information conveyed in the systematic risk of an investment is rather limited.